Is $\left\lVert x \right\rVert*x$ a function of class $C^{\infty}$

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I just liked to know if that function ($\left\lVert x \right\rVert*x$) is of class $C^{\infty}$ in $x=0$. I think it is'nt, and I proved that, but my teacher said me to prove that this function is of this class. Please tell me what you think about.